Base field 4.4.5744.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[43, 43, -w - 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 36x^{8} + 466x^{6} - 2588x^{4} + 5293x^{2} - 384\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{3} + 4w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{1}{64}e^{9} - \frac{31}{64}e^{7} + \frac{319}{64}e^{5} - \frac{1209}{64}e^{3} + \frac{137}{8}e$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{64}e^{9} - \frac{31}{64}e^{7} + \frac{311}{64}e^{5} - \frac{1049}{64}e^{3} + \frac{27}{4}e$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w]$ | $-\frac{1}{32}e^{8} + \frac{31}{32}e^{6} - \frac{311}{32}e^{4} + \frac{1033}{32}e^{2} - 8$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + \frac{91}{8}e$ |
| 17 | $[17, 17, -w^{2} + 2]$ | $\phantom{-}\frac{1}{32}e^{9} - \frac{31}{32}e^{7} + \frac{315}{32}e^{5} - \frac{1145}{32}e^{3} + \frac{227}{8}e$ |
| 19 | $[19, 19, -w^{3} + 5w]$ | $-\frac{1}{2}e^{3} + \frac{11}{2}e$ |
| 31 | $[31, 31, -w^{2} + 2w + 3]$ | $-\frac{7}{64}e^{8} + \frac{201}{64}e^{6} - \frac{1809}{64}e^{4} + \frac{5119}{64}e^{2} - 2$ |
| 37 | $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ | $-\frac{1}{64}e^{9} + \frac{31}{64}e^{7} - \frac{319}{64}e^{5} + \frac{1209}{64}e^{3} - \frac{137}{8}e$ |
| 43 | $[43, 43, -w - 3]$ | $-1$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{1}{64}e^{9} - \frac{31}{64}e^{7} + \frac{335}{64}e^{5} - \frac{1561}{64}e^{3} + \frac{363}{8}e$ |
| 53 | $[53, 53, w^{3} - 6w - 2]$ | $\phantom{-}\frac{5}{32}e^{8} - \frac{151}{32}e^{6} + \frac{1443}{32}e^{4} - \frac{4353}{32}e^{2} + 6$ |
| 59 | $[59, 59, 2w^{3} - w^{2} - 10w - 2]$ | $-\frac{3}{32}e^{8} + \frac{89}{32}e^{6} - \frac{837}{32}e^{4} + \frac{2559}{32}e^{2} - 12$ |
| 61 | $[61, 61, 2w^{3} - w^{2} - 10w]$ | $\phantom{-}\frac{1}{16}e^{8} - \frac{27}{16}e^{6} + \frac{223}{16}e^{4} - \frac{549}{16}e^{2} - 8$ |
| 61 | $[61, 61, 2w^{3} - w^{2} - 8w]$ | $\phantom{-}\frac{1}{32}e^{9} - \frac{31}{32}e^{7} + \frac{307}{32}e^{5} - \frac{985}{32}e^{3} + \frac{37}{8}e$ |
| 71 | $[71, 71, 2w^{3} - 9w - 2]$ | $\phantom{-}\frac{1}{4}e^{5} - 5e^{3} + \frac{91}{4}e$ |
| 73 | $[73, 73, -w^{3} - w^{2} + 6w + 3]$ | $\phantom{-}\frac{1}{8}e^{5} - \frac{5}{2}e^{3} + \frac{99}{8}e$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{5}{64}e^{8} - \frac{139}{64}e^{6} + \frac{1187}{64}e^{4} - \frac{3117}{64}e^{2} - 2$ |
| 83 | $[83, 83, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}\frac{1}{32}e^{9} - \frac{31}{32}e^{7} + \frac{311}{32}e^{5} - \frac{1033}{32}e^{3} + 8e$ |
| 101 | $[101, 101, 2w^{3} - 8w - 3]$ | $\phantom{-}\frac{3}{8}e^{5} - 8e^{3} + \frac{293}{8}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $43$ | $[43, 43, -w - 3]$ | $1$ |